Abstract
Precision agriculture requires many local measurements. Sometimes two measurements are available: a low-cost noisy measurement and an accurate expensive one. For example, soil testing in a laboratory is expensive and accurate. On-the-go pH meters are available, but they are not as accurate. The question addressed here is what is the best way to combine these measures to guide precision applications? The first step is to estimate the joint spatial distribution of the two measures. The joint distribution is estimated using Bayesian Kriging since it can consider the information when the measures are spatially autocorrelated. The second step is to determine the economic optimum of how many of each measure to use. This study obtained the ratio of expensive and accurate measurements by maximizing the expected net present value using Bayesian Decision Theory and a grid search procedure. To demonstrate the method, a harmonization process that uses no spatial information was compared with Bayesian Kriging using Monte Carlo data. A wheat production example was used to parameterize the Monte Carlo simulation. Soil pH lab sampling and on-the-go soil pH sensors were simulated as the two different measurements for soil mapping in wheat fields. Bayesian Kriging led to more accurate soil mapping and a higher expected net present value.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The lower bounds for the spatial correlation, precision, sensitivity change of low-cost measurement, and standard deviation of low-cost measurement error parameters were set to zero, meaning non-negativity constraints. The upper bounds were also set to reduce the program execution time for convergence. This study set the upper bounds to be large enough, with spatial correlation parameter set to 1 and the other three to 10. For the bias parameter, lower and upper bounds set to ± 10.
For the Bayesian Kriging estimation, 10,000 iterations each for four MCMC chains were used. The first 5,000 observations were burned in, so 5,000 iterations of each chain, total 20,000 samples were used.
The percentage of expensive measurements for maximum NPV remained at 2% regardless of error sizes of accurate measurements, although the dollars had changed.
References
Adamchuk, V. I., Morgan, M. T., & Lowenberg-Deboer, J. M. (2004). A model for agro-economic analysis of soil pH mapping. Precision Agriculture, 5(2), 111–129. https://doi.org/10.1016/j.compag.2004.03.002
Caubet, M., Dobarco, M. R., Arrouays, D., Minasny, B., & Saby, N. P. (2019). Merging country, continental and global predictions of soil texture: Lessons from ensemble modelling in France. Geoderma, 337, 99–110. https://doi.org/10.1016/j.geoderma.2018.09.007
Cho, W., & Brorsen, B. W. (2021). Design of the rainfall index crop insurance program for pasture, rangeland, and forage. Journal of Agricultural and Resource Economics, 46(1), 85–100.
Cho, W., Brorsen, B. W., & Arnall, D. B. (2020). Banding of phosphorus as an alternative to lime for wheat in acid soil. Agrosystems, Geosciences & Environment, 3(1), e20071. https://doi.org/10.1002/agg2.20071
Cho, W., Brorsen, B. W., Biermacher, J. T., & Rogers, J. K. (2019). Rising plate meter calibrations for forage mass of wheat and rye. Agricultural & Environmental Letters. https://doi.org/10.2134/ael2018.11.0057
Eckert, D., & Sims, J. T. (2009). Recommended soil pH and lime requirement tests. In J. T. Sims & A. Wolf (Eds.), Recommended Soil Testing Procedures for the Northeastern United States. Northeastern Regional Publication No. 493 (pp. 11–16). Newark, DE, USA: The Northeast Coordinating Committee for Soil Testing.
Ge, Y., Avitabile, V., Heuvelink, G. B., Wang, J., & Herold, M. (2014). Fusion of pan-tropical biomass maps using weighted averaging and regional calibration data. International Journal of Applied Earth Observation and Geoinformation, 31, 13–24. https://doi.org/10.1016/j.jag.2014.02.011
Heuvelink, G. B. M., & Bierkens, M. F. P. (1992). Combining soil maps with interpolations from point observations to predict quantitative soil properties. Geoderma, 55(1–2), 1–15. https://doi.org/10.1016/0016-7061(92)90002-O
Leroux, C., Jones, H., Pichon, L., Taylor, J., & Tisseyre, B. (2019). Automatic harmonization of heterogeneous agronomic and environmental spatial data. Precision Agriculture, 20(6), 1211–1230. https://doi.org/10.1007/s11119-019-09650-0
Lollato, R. P., Ochsner, T. E., Arnall, D. B., Griffin, T. W., & Edwards, J. T. (2019). From field experiments to regional forecasts: Upscaling wheat grain and forage yield response to acidic soils. Agronomy Journal, 111(1), 287–302. https://doi.org/10.2134/agronj2018.03.0206
Maldaner, L. F., Molin, J. P., & Canata, T. F. (2016). Processing yield data from two or more combines. In Proceedings of the 13th international conference on precision agriculture. Retrieved January, 2022, from http://afurlan.com.br/lap/cp/assets/layout/files/tc/pub_processing-yield-data-from-two-or-more-combines---maldaner-l-f-molin-j-p-canata-t-f---icpa-2016-01-11-2016.pdf
Malone, B. P., Minasny, B., Odgers, N. P., & McBratney, A. B. (2014). Using model averaging to combine soil property rasters from legacy soil maps and from point data. Geoderma, 232, 34–44. https://doi.org/10.1016/j.geoderma.2014.04.033
Nawi, N. M., Chen, G., & Jensen, T. (2014). In-field measurement and sampling technologies for monitoring quality in the sugarcane industry: A review. Precision Agriculture, 15(6), 684–703. https://doi.org/10.1007/s11119-014-9362-9
Park, E., Brorsen, B. W., & Harri, A. (2019). Using Bayesian Kriging for spatial smoothing in crop insurance rating. American Journal of Agricultural Economics, 101(1), 330–351. https://doi.org/10.1093/ajae/aay045
Park, E., Brorsen, B. W., & Harri, A. (2020). Spatially smoothed crop yield density: Physical distance vs climate similarity. Journal of Agricultural and Resource Economics, 45(3), 533–548.
Park, E., Harri, A., & Coble, K. H. (2021). Estimating crop yield densities for counties with missing data. Journal of Agricultural and Resource Economics. https://doi.org/10.22004/ag.econ.313319
Pichon, L., Leroux, C., Geraudie, V., Taylor, J., & Tisseyre, B. (2019). Investigating the harmonization of highly noisy heterogeneous datasets hand-collected over the same study domain. Precision Agriculture, 19, 735–741.
Poursina, D., and Brorsen, B. W. (2021). Site-specific nitrogen recommendation: Using Bayesian Kriging method with different correlation matrices. Agricultural and Applied Economics Association annual meeting, Austin, TX. https://ageconsearch.umn.edu/record/312653/files/Poursina.pdf
Purcell, D. E., Leonard, G. J., O’Shea, M. G., & Kokot, S. (2005). A chemometrics investigation of sugarcane plant properties based on the molecular composition of epicuticular wax. Chemometrics and Intelligent Laboratory Systems, 76(2), 135–147. https://doi.org/10.1016/j.chemolab.2004.10.004
Sams, B., Litchfield, C., Sanchez, L., & Dokoozlian, N. (2017). Two methods for processing yield maps from multiple sensors in large vineyards in California. Advances in Animal Biosciences, 8(2), 530–533. https://doi.org/10.1017/S2040470017000516
Schirrmann, M., Gebbers, R., Kramer, E., & Seidel, J. (2011). Soil pH mapping with an on-the-go sensor. Sensors, 11(1), 573–598. https://doi.org/10.3390/s110100573
Sollenberger, L. E., & Cherney, D. J. R. (1995). Evaluating forage production and quality. In: R.F. Barnes, D.A. Miller, & C.J. Nelson (Eds) Forages Vol. II. The science of grassland agriculture 5th edition (pp. 97–110). Ames, IA, USA: Iowa State University Press
Stan Development Team. (2020). RStan: The R interface to Stan. R package version 2.21.2, http://mc-stan.org/.
Thomas, G. W. (1996). Soil pH and soil acidity. In: J. M. Bartels (Ed) Methods of Soil Analysis. Part 3 Chemical Methods (pp. 11–16). Madison, WI, USA: SSSA-ASA.
U.S. Department of Agriculture Farm Service Agency. (2021). Farm Loan Programs. Retrieved from https://www.fsa.usda.gov/programs-and-services/farm-loan-programs/
Zhang, H., & McCray, B. (2018). Oklahoma Agricultural Soil Test Summary 2014–2017. OSU Extension Fact Sheets CR-2283, Oklahoma State University. https://extension.okstate.edu/fact-sheets/oklahoma-agricultural-soil-test-summary-2014-2017.html#:~:text=The%20median%20pH%20of%20Oklahoma,a%20pH%20less%20than%206.3.
Zhang, H., Raun, B., & Arnall, B. (2017). Oklahoma soil test interpretations. OSU Extension Fact Sheets PSS-2225, Oklahoma State University. http://factsheets.okstate.edu/documents/pss-2225-osu-soil-test-interpretations/
Acknowledgements
The research was primarily funded by the A.J. & Susan Jacques Chair. Brorsen also receives funding from the Oklahoma Agricultural Experiment Station and USDA National Institute of Food and Agriculture, Hatch Project Number OKL03170.
Funding
Funding was provided by Oklahoma Agricultural Experiment Station, A.J. & Susan Jacques Chair, and USDA National Institute of Food and Agriculture (OKL03170).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cho, W., ShalekBriski, A., Brorsen, B.W. et al. Combining low-cost noisy measurements with expensive accurate measurements to guide precision applications. Precision Agric 23, 2215–2228 (2022). https://doi.org/10.1007/s11119-022-09917-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11119-022-09917-z